Subgroups — #6464980

Order 512.

1525 conjugacy classes of subgroups.

The subgroup lattice has 1227 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34969	C₂	1	1	yes	maximal, characteristic, complemented
2	#34915	C₂	1	1	yes	maximal, characteristic, complemented
3	#29090	C₂	1	1	yes	maximal, characteristic, complemented
4	#29087	C₂	1	1	yes	maximal, characteristic, complemented
5	#29046	C₂	1	1	yes	maximal, characteristic, complemented
6	#29040	C₂	1	1	yes	maximal, characteristic, complemented
7	#29035	C₂	1	1	yes	maximal, characteristic, complemented
8	#29033	C₂	1	1	yes	maximal, characteristic, complemented
9	#28986	C₂	1	1	yes	maximal, characteristic, complemented
10	#28983	C₂	1	1	yes	maximal, characteristic
11	#28018	C₂	1	1	yes	maximal, characteristic, complemented
12	#28002	C₂	1	1	yes	maximal, characteristic, complemented
13	#27837	C₂	1	1	yes	maximal, characteristic, complemented
14	#27800	C₂	1	1	yes	maximal, characteristic, complemented
15	#26486	C₂	1	1	yes	maximal, characteristic, complemented
16	#26261	C₂	1	1	yes	maximal, characteristic, complemented
17	#25411	C₂	1	1	yes	maximal, characteristic
18	#25041	C₂	1	1	yes	maximal, characteristic, complemented
19	#23826	C₂	1	1	yes	maximal, characteristic, complemented
20	#23821	C₂	1	1	yes	maximal, characteristic, complemented
21	#23709	C₂	1	1	yes	maximal, characteristic, complemented
22	#23708	C₂	1	1	yes	maximal, characteristic
23	#21731	C₂	1	1	yes	maximal, characteristic, complemented
24	#21693	C₂	1	1	yes	maximal, characteristic, complemented
25	#21528	C₂	1	1	yes	maximal, characteristic, complemented
26	#21528	C₂	1	1	yes	maximal, characteristic, complemented
27	#21288	C₂	1	1	yes	maximal, characteristic, complemented
28	#21123	C₂	1	1	yes	maximal, characteristic, complemented
29	#21122	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#440	C₂	1	1	yes	maximal, characteristic, complemented
31	#20479	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#501	C₂²	1	1	yes	characteristic
33	C₂×#495	C₂²	1	1	yes	characteristic
34	C₂×#465	C₂²	1	1	yes	characteristic
35	C₂×#465	C₂²	1	1	yes	characteristic
36	C₂×#442	C₂²	1	1	yes	characteristic
37	C₂×#441	C₂²	1	1	yes	characteristic
38	C₂×#440	C₂²	1	1	yes	characteristic
39	C₂×#440	C₂²	1	1	yes	characteristic
40	C₂×#440	C₂²	1	1	yes	characteristic
41	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
42	C₂×#432	C₂²	1	1	yes	characteristic
43	C₂²×#97	C₂²	1	1	yes	characteristic
44	#2597	—	2	1	no	—
45	#2596	—	2	1	no	—
46	#2595	—	2	1	no	—
47	#2594	—	2	1	no	—
48	#2530	—	2	1	no	—
49	#2527	—	2	1	no	—
50	#2513	C₂²	1	1	yes	characteristic
51	#2511	C₂²	1	1	yes	characteristic
52	#2509	C₂²	1	1	yes	characteristic
53	#2509	C₂²	1	1	yes	characteristic
54	#2494	C₂²	1	1	yes	characteristic
55	#2494	C₂²	1	1	yes	characteristic
56	#2492	C₂²	1	1	yes	characteristic
57	#2490	C₂²	1	1	yes	characteristic
58	#2477	—	2	1	no	—
59	#2470	—	2	1	no	—
60	#2453	C₂²	1	1	yes	characteristic
61	#2452	C₂²	1	1	yes	characteristic
62	#2448	C₂²	1	1	yes	characteristic
63	#2447	C₂²	1	1	yes	characteristic
64	#2427	C₂²	1	1	yes	characteristic
65	#2426	C₂²	1	1	yes	characteristic
66	#2422	C₂²	1	1	yes	characteristic
67	#2421	C₂²	1	1	yes	characteristic
68	#2401	—	2	1	no	—
69	#2401	—	2	1	no	—
70	#2398	—	2	1	no	—
71	#2395	—	2	1	no	—
72	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
73	C₄×#125	C₂²	1	1	yes	characteristic
74	C₄×#124	C₂²	1	1	yes	characteristic
75	C₄×#124	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊Q₈	—	2	1	no	—
77	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
78	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
79	C₄×#123	—	2	1	no	—
80	C₄×#121	C₂²	1	1	yes	characteristic
81	C₄×#121	C₂²	1	1	yes	characteristic
82	#2298	—	2	1	no	—
83	#2295	C₂²	1	1	yes	characteristic
84	#2293	—	2	1	no	—
85	#2293	C₂²	1	1	yes	characteristic
86	C₄²×Q₈	C₂²	1	1	yes	characteristic
87	C₄²×D₄	C₂²	1	1	yes	characteristic
88	C₄×#117	C₂²	1	1	yes	characteristic
89	#2101	C₂²	1	1	yes	characteristic
90	#2101	C₂²	1	1	yes	characteristic
91	#2101	C₂²	1	1	yes	characteristic
92	#2101	C₂²	1	1	yes	characteristic
93	#2088	C₂²	1	1	yes	characteristic
94	#2088	C₂²	1	1	yes	characteristic
95	#2077	C₂²	1	1	yes	characteristic
96	#2077	C₂²	1	1	yes	characteristic
97	#2074	C₂²	1	1	yes	characteristic
98	#2073	C₂²	1	1	yes	characteristic
99	#2072	C₂²	1	1	yes	characteristic
100	#2071	C₂²	1	1	yes	characteristic
101	#2068	C₂²	1	1	yes	characteristic
102	#2067	C₂²	1	1	yes	characteristic
103	#2066	C₂²	1	1	yes	characteristic
104	#2065	C₂²	1	1	yes	characteristic
105	#2056	C₂²	1	1	yes	characteristic
106	#2054	C₂²	1	1	yes	characteristic
107	#2042	C₂²	1	1	yes	characteristic
108	#2042	C₂²	1	1	yes	characteristic
109	#2042	C₂²	1	1	yes	characteristic
110	#2042	C₂²	1	1	yes	characteristic
111	#2036	C₂²	1	1	yes	characteristic
112	#2035	C₂²	1	1	yes	characteristic
113	#2034	C₂²	1	1	yes	characteristic
114	#2033	C₂²	1	1	yes	characteristic
115	#2026	C₂²	1	1	yes	characteristic
116	#2025	C₂²	1	1	yes	characteristic
117	#2024	C₂²	1	1	yes	characteristic
118	#2023	C₂²	1	1	yes	characteristic
119	#2001	C₂²	1	1	yes	characteristic
120	#1999	C₂²	1	1	yes	characteristic
121	#1993	C₂²	1	1	yes	characteristic
122	#1992	C₂²	1	1	yes	characteristic
123	#1973	C₂²	1	1	yes	characteristic
124	#1973	C₂²	1	1	yes	characteristic
125	#1973	C₂²	1	1	yes	characteristic
126	#1973	C₂²	1	1	yes	characteristic
127	#1973	C₂²	1	1	yes	characteristic
128	#1972	C₂²	1	1	yes	characteristic
129	#1971	C₂²	1	1	yes	characteristic
130	#1968	C₂²	1	1	yes	characteristic
131	#1958	C₂²	1	1	yes	characteristic
132	#1958	C₂²	1	1	yes	characteristic
133	#1944	C₂²	1	1	yes	characteristic
134	#1944	C₂²	1	1	yes	characteristic
135	#1943	C₂²	1	1	yes	characteristic
136	#1942	C₂²	1	1	yes	characteristic
137	#1942	C₂²	1	1	yes	characteristic
138	#1942	C₂²	1	1	yes	characteristic
139	#1941	C₂²	1	1	yes	characteristic
140	#1941	C₂²	1	1	yes	characteristic
141	#1936	C₂²	1	1	yes	characteristic
142	#1936	C₂²	1	1	yes	characteristic
143	#1936	C₂²	1	1	yes	characteristic
144	#1935	C₂²	1	1	yes	characteristic
145	#1935	C₂²	1	1	yes	characteristic
146	#1935	C₂²	1	1	yes	characteristic
147	#1934	C₂²	1	1	yes	characteristic
148	#1933	C₂²	1	1	yes	characteristic
149	#1928	C₂²	1	1	yes	characteristic
150	#1927	C₂²	1	1	yes	characteristic
151	#1926	C₂²	1	1	yes	characteristic
152	#1925	C₂²	1	1	yes	characteristic
153	#1920	C₂²	1	1	yes	characteristic
154	#1920	C₂²	1	1	yes	characteristic
155	#1919	C₂²	1	1	yes	characteristic
156	#1919	C₂²	1	1	yes	characteristic
157	#1893	C₂²	1	1	yes	characteristic
158	#1893	C₂²	1	1	yes	characteristic
159	#1892	C₂²	1	1	yes	characteristic
160	#1892	C₂²	1	1	yes	characteristic
161	#1879	C₂²	1	1	yes	characteristic
162	#1879	C₂²	1	1	yes	characteristic
163	#1878	C₂²	1	1	yes	characteristic
164	#1878	C₂²	1	1	yes	characteristic
165	#1865	C₂²	1	1	yes	characteristic
166	#1864	C₂²	1	1	yes	characteristic
167	#1863	C₂²	1	1	yes	characteristic
168	#1862	C₂²	1	1	yes	characteristic
169	#1847	C₂²	1	1	yes	characteristic
170	#1846	C₂²	1	1	yes	characteristic
171	#1808	C₂²	1	1	yes	characteristic
172	#1808	C₂²	1	1	yes	characteristic
173	#1776	C₂²	1	1	yes	characteristic
174	#1776	C₂²	1	1	yes	characteristic
175	#1776	C₂²	1	1	yes	characteristic
176	#1776	C₂²	1	1	yes	characteristic
177	#1776	C₂²	1	1	yes	characteristic
178	C₄×#107	C₂²	1	1	yes	characteristic
179	#1771	C₂²	1	1	yes	characteristic
180	#1771	C₂²	1	1	yes	characteristic
181	#1771	C₂²	1	1	yes	characteristic
182	#1771	C₂²	1	1	yes	characteristic
183	#1763	C₂²	1	1	yes	characteristic
184	#1763	C₂²	1	1	yes	characteristic
185	#1763	C₂²	1	1	yes	characteristic
186	#1763	C₂²	1	1	yes	characteristic
187	#1763	C₂²	1	1	yes	characteristic
188	#1762	C₂²	1	1	yes	characteristic
189	#1762	C₂²	1	1	yes	characteristic
190	#1762	C₂²	1	1	yes	characteristic
191	#1762	C₂²	1	1	yes	characteristic
192	#1762	C₂²	1	1	yes	characteristic
193	C₄×#103	C₂²	1	1	yes	characteristic
194	C₄×#102	C₂²	1	1	yes	characteristic
195	#1752	C₂²	1	1	yes	characteristic
196	#1752	C₂²	1	1	yes	characteristic
197	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
198	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
199	#1745	C₂²	1	1	yes	characteristic
200	#1745	C₂²	1	1	yes	characteristic
201	C₄×#97	C₂²	1	1	yes	characteristic
202	C₄×#97	C₂²	1	1	yes	characteristic
203	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
204	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂²×D₈	C₂³	1	1	yes	characteristic
207	C₂³×C₈	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×#125	C₂³	1	1	yes	characteristic
211	C₂×#124	C₂³	1	1	yes	characteristic
212	C₂×#124	C₂³	1	1	yes	characteristic
213	C₂×#123	—	2	1	no	—
214	C₂×C₂²⋊Q₈	—	2	1	no	—
215	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×#121	C₂³	1	1	yes	characteristic
218	C₂×#121	C₂³	1	1	yes	characteristic
219	C₂×C₄×Q₈	—	2	1	no	—
220	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	—	2	1	no	—
226	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
230	C₂×#117	—	2	1	no	—
231	C₂×#117	D₄	1	1	yes	characteristic
232	C₂×#117	D₄	1	1	yes	characteristic
233	C₂²×C₄²	—	2	1	no	—
234	C₂²×C₄²	C₂³	1	1	yes	characteristic
235	#501	—	2	4	no	—
236	#495	—	2	4	no	—
237	#465	—	2	4	no	—
238	#465	—	2	4	no	—
239	#442	—	2	4	no	—
240	#441	—	2	4	no	—
241	#440	—	2	4	no	—
242	#440	—	2	4	no	—
243	#440	—	2	4	no	—
244	C₄×SD₁₆	—	2	4	no	—
245	#432	—	2	4	no	—
246	C₂×#107	C₂³	1	1	yes	characteristic
247	C₂×#107	C₂³	1	1	yes	characteristic
248	C₂×#107	C₂³	1	1	yes	characteristic
249	C₂×#107	C₂³	1	1	yes	characteristic
250	C₂×#107	C₂³	1	1	yes	characteristic
251	C₂×#107	C₂³	1	1	yes	characteristic
252	C₂×#106	C₂³	1	1	yes	characteristic
253	C₂×#106	C₂³	1	1	yes	characteristic
254	C₂×#106	C₂³	1	1	yes	characteristic
255	C₂×#106	C₂³	1	1	yes	characteristic
256	C₂×#106	C₂³	1	1	yes	characteristic
257	C₂×#106	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂×#103	C₂³	1	1	yes	characteristic
261	C₂×#103	C₂³	1	1	yes	characteristic
262	C₂×#103	C₂³	1	1	yes	characteristic
263	C₂×#103	C₂³	1	1	yes	characteristic
264	C₂×#103	C₂³	1	1	yes	characteristic
265	C₂×#103	C₂³	1	1	yes	characteristic
266	C₂×#103	C₂³	1	1	yes	characteristic
267	C₂×#103	C₂³	1	1	yes	characteristic
268	C₂×#103	C₂³	1	1	yes	characteristic
269	C₂×#103	C₂³	1	1	yes	characteristic
270	C₂×#103	C₂³	1	1	yes	characteristic
271	C₂×#103	C₂³	1	1	yes	characteristic
272	C₂×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	C₂³	1	1	yes	characteristic
275	C₂×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×#102	C₂³	1	1	yes	characteristic
283	C₂×#102	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂×#97	—	2	4	no	—
287	C₂×#97	C₂³	1	1	yes	characteristic
288	C₂×#97	C₂³	1	1	yes	characteristic
289	C₂×#97	C₂³	1	1	yes	characteristic
290	C₂×#97	C₂³	1	1	yes	characteristic
291	C₂×#97	C₂³	1	1	yes	characteristic
292	C₂×#97	C₂³	1	1	yes	characteristic
293	C₂×#97	C₂³	1	1	yes	characteristic
294	C₂×#97	C₂³	1	1	yes	characteristic
295	C₂×#97	C₂³	1	1	yes	characteristic
296	C₂×#97	C₂³	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
298	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
301	#401	—	2	1	no	—
302	#401	—	2	1	no	—
303	#400	—	2	1	no	—
304	#400	—	2	1	no	—
305	#400	—	2	1	no	—
306	#400	—	2	1	no	—
307	#400	—	2	1	no	—
308	#400	—	2	1	no	—
309	#400	—	2	1	no	—
310	#400	—	2	1	no	—
311	#400	—	2	1	no	—
312	#399	—	2	1	no	—
313	#398	—	2	1	no	—
314	#397	—	2	1	no	—
315	#397	—	2	1	no	—
316	#397	—	2	1	no	—
317	#397	—	2	1	no	—
318	#397	—	2	1	no	—
319	#397	—	2	1	no	—
320	#397	—	2	1	no	—
321	#397	—	2	1	no	—
322	#397	—	2	1	no	—
323	#397	—	2	1	no	—
324	#397	—	2	1	no	—
325	#396	—	2	1	no	—
326	#396	—	2	1	no	—
327	#394	—	2	1	no	—
328	#394	—	2	1	no	—
329	#394	—	2	1	no	—
330	#394	—	2	1	no	—
331	#393	—	2	1	no	—
332	#393	—	2	1	no	—
333	#391	—	2	1	no	—
334	#391	—	2	1	no	—
335	#391	C₂³	1	1	yes	characteristic
336	#391	C₂³	1	1	yes	characteristic
337	#391	C₂³	1	1	yes	characteristic
338	#391	C₂³	1	1	yes	characteristic
339	#391	C₂³	1	1	yes	characteristic
340	#391	C₂³	1	1	yes	characteristic
341	#390	—	2	1	no	—
342	#390	—	2	1	no	—
343	#390	C₂³	1	1	yes	characteristic
344	#390	C₂³	1	1	yes	characteristic
345	#390	C₂³	1	1	yes	characteristic
346	#390	C₂³	1	1	yes	characteristic
347	#390	C₂³	1	1	yes	characteristic
348	#390	C₂³	1	1	yes	characteristic
349	#389	—	2	1	no	—
350	#389	—	2	1	no	—
351	#389	—	2	1	no	—
352	#389	—	2	1	no	—
353	#389	C₂³	1	1	yes	characteristic
354	#389	C₂³	1	1	yes	characteristic
355	#389	C₂³	1	1	yes	characteristic
356	#389	C₂³	1	1	yes	characteristic
357	#389	C₂³	1	1	yes	characteristic
358	#389	C₂³	1	1	yes	characteristic
359	#389	C₂³	1	1	yes	characteristic
360	#389	C₂³	1	1	yes	characteristic
361	#389	C₂³	1	1	yes	characteristic
362	#389	C₂³	1	1	yes	characteristic
363	#389	C₂³	1	1	yes	characteristic
364	#389	C₂³	1	1	yes	characteristic
365	#388	—	2	1	no	—
366	#388	—	2	1	no	—
367	#388	—	2	1	no	—
368	#388	—	2	1	no	—
369	#388	—	2	1	no	—
370	#388	—	2	1	no	—
371	#388	—	2	1	no	—
372	#388	—	2	1	no	—
373	#388	—	2	1	no	—
374	#388	—	2	1	no	—
375	#388	—	2	1	no	—
376	#388	—	2	1	no	—
377	#388	—	2	1	no	—
378	#388	—	2	1	no	—
379	#388	—	2	1	no	—
380	#388	—	2	1	no	—
381	#388	—	2	1	no	—
382	#388	—	2	1	no	—
383	#387	—	2	1	no	—
384	#387	—	2	1	no	—
385	#387	—	2	1	no	—
386	#387	—	2	1	no	—
387	#387	—	2	1	no	—
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	#387	—	2	1	no	—
392	#387	—	2	1	no	—
393	#387	—	2	1	no	—
394	#387	—	2	1	no	—
395	#387	—	2	1	no	—
396	#387	—	2	1	no	—
397	#386	—	2	1	no	—
398	#386	—	2	1	no	—
399	#386	—	2	1	no	—
400	#385	—	2	1	no	—
401	#385	—	2	1	no	—
402	#385	—	2	1	no	—
403	#385	—	2	1	no	—
404	#385	—	2	1	no	—
405	#384	C₂³	1	1	yes	characteristic
406	#382	C₂³	1	1	yes	characteristic
407	#382	C₂³	1	1	yes	characteristic
408	#382	C₂³	1	1	yes	characteristic
409	#381	—	2	1	no	—
410	#380	—	2	1	no	—
411	#380	C₂³	1	1	yes	characteristic
412	#380	C₂³	1	1	yes	characteristic
413	#380	C₂³	1	1	yes	characteristic
414	#380	C₂³	1	1	yes	characteristic
415	C₄×C₄⋊C₄	—	2	1	no	—
416	C₄×C₄⋊C₄	—	2	1	no	—
417	C₄×C₄⋊C₄	—	2	1	no	—
418	C₄×C₄⋊C₄	—	2	1	no	—
419	C₄×C₄⋊C₄	—	2	1	no	—
420	C₄×C₄⋊C₄	—	2	1	no	—
421	C₄×C₄⋊C₄	—	2	1	no	—
422	C₄×C₄⋊C₄	—	2	1	no	—
423	C₄×C₄⋊C₄	—	2	1	no	—
424	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
425	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
428	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
430	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
431	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
432	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
436	C₄×C₂²⋊C₄	—	2	1	no	—
437	C₄×C₂²⋊C₄	—	2	1	no	—
438	C₄×C₂²⋊C₄	—	2	1	no	—
439	C₄×C₂²⋊C₄	—	2	1	no	—
440	C₄×C₂²⋊C₄	—	2	1	no	—
441	C₄×C₂²⋊C₄	—	2	1	no	—
442	C₄×C₂²⋊C₄	—	2	1	no	—
443	C₄×C₂²⋊C₄	—	2	1	no	—
444	C₄×C₂²⋊C₄	—	2	1	no	—
445	C₄×C₂²⋊C₄	—	2	1	no	—
446	C₄×C₂²⋊C₄	—	2	1	no	—
447	C₄×C₂²⋊C₄	—	2	1	no	—
448	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
451	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
452	#376	—	2	1	no	—
453	#376	D₄	1	1	yes	characteristic
454	#376	D₄	1	1	yes	characteristic
455	C₄³	—	2	1	no	—
456	C₄³	C₂³	1	1	yes	characteristic
457	C₄³	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	C₂²×Q₈	—	2	1	no	—
491	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
492	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	C₂⁴	1	1	yes	characteristic
496	C₂²×D₄	C₂⁴	1	1	yes	characteristic
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
502	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
503	C₂³×C₄	C₂⁴	1	1	yes	characteristic
504	C₂×Q₁₆	—	2	2	no	—
505	C₂×Q₁₆	—	2	2	no	—
506	C₂×Q₁₆	—	4	1	no	—
507	C₂×SD₁₆	—	2	2	no	—
508	C₂×SD₁₆	—	2	2	no	—
509	C₂×SD₁₆	—	2	2	no	—
510	C₂×SD₁₆	—	2	2	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	#41	1	4	yes	—
513	C₂×D₈	—	2	2	no	—
514	C₂×D₈	—	2	2	no	—
515	C₂×D₈	—	4	1	no	—
516	C₂²×C₈	—	2	2	no	—
517	C₂²×C₈	—	2	2	no	—
518	C₂²×C₈	—	2	2	no	—
519	C₂²×C₈	—	2	2	no	—
520	C₂²×C₈	—	4	1	no	—
521	C₂²×C₈	—	4	1	no	—
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	C₂²×C₈	C₂⁴	1	1	yes	characteristic
527	C₂²×C₈	C₂⁴	1	1	yes	characteristic
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₄⋊Q₈	—	2	2	no	—
531	C₄⋊Q₈	—	4	1	no	—
532	#125	—	2	2	no	—
533	#125	—	4	1	no	—
534	#124	—	2	2	no	—
535	#124	—	2	2	no	—
536	#124	—	4	1	no	—
537	#124	—	4	1	no	—
538	#123	—	4	4	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	4	1	no	—
542	C₂²⋊Q₈	—	4	1	no	—
543	C₂²⋊Q₈	—	4	4	no	—
544	#121	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	—	4	1	no	—
547	#121	—	4	1	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	4	1	no	—
555	C₄×Q₈	—	4	1	no	—
556	C₄×Q₈	—	8	2	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	4	1	no	—
564	C₄×D₄	—	4	1	no	—
565	C₄×D₄	—	4	4	no	—
566	C₄×D₄	—	8	2	no	—
567	#117	—	4	2	no	—
568	#117	—	4	4	no	—
569	#117	—	4	2	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
641	C₂×C₄²	—	2	2	no	—
642	C₂×C₄²	—	2	2	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	—	2	1	no	—
651	C₂×C₄²	—	2	1	no	—
652	C₂×C₄²	—	2	1	no	—
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	—	8	2	no	—
656	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
657	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
658	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
660	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
663	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
664	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
665	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
666	C₂×C₄²	C₂⁴	1	1	yes	characteristic
667	C₂×C₄²	C₂⁴	1	1	yes	characteristic
668	C₂×C₄²	C₂⁴	1	1	yes	characteristic
669	C₂×C₄²	C₂⁴	1	1	yes	characteristic
670	C₂×C₄²	C₂⁴	1	1	yes	characteristic
671	C₂×C₄²	C₂⁴	1	1	yes	characteristic
672	#107	—	2	2	no	—
673	#107	—	2	2	no	—
674	#107	—	2	2	no	—
675	#107	—	2	2	no	—
676	#107	—	2	2	no	—
677	#107	—	4	1	no	—
678	#106	—	2	2	no	—
679	#106	—	2	2	no	—
680	#106	—	2	2	no	—
681	#106	—	2	2	no	—
682	#106	—	4	1	no	—
683	#106	#41	1	4	yes	—
684	C₄⋊C₈	—	2	2	no	—
685	C₄⋊C₈	—	2	2	no	—
686	#103	—	2	2	no	—
687	#103	—	2	2	no	—
688	#103	—	2	2	no	—
689	#103	—	2	2	no	—
690	#103	—	2	2	no	—
691	#103	—	2	2	no	—
692	#103	—	2	2	no	—
693	#103	—	2	2	no	—
694	#103	—	4	1	no	—
695	#103	—	4	1	no	—
696	#103	—	4	1	no	—
697	#103	—	4	1	no	—
698	#102	—	2	2	no	—
699	#102	—	2	2	no	—
700	#102	—	2	2	no	—
701	#102	—	2	2	no	—
702	#102	—	2	2	no	—
703	#102	—	2	2	no	—
704	#102	—	2	2	no	—
705	#102	—	2	2	no	—
706	#102	—	4	1	no	—
707	#102	—	4	1	no	—
708	#102	—	4	1	no	—
709	#102	—	4	1	no	—
710	C₂²⋊C₈	—	2	2	no	—
711	C₂²⋊C₈	—	2	2	no	—
712	#97	—	2	2	no	—
713	#97	—	2	2	no	—
714	#97	—	2	2	no	—
715	#97	—	2	2	no	—
716	#97	—	2	2	no	—
717	#97	—	2	2	no	—
718	#97	—	4	1	no	—
719	#97	—	4	1	no	—
720	#97	#41	1	4	yes	—
721	#97	#41	1	4	yes	—
722	C₄×C₈	—	2	2	no	—
723	C₄×C₈	—	2	2	no	—
724	C₄×C₈	—	4	1	no	—
725	C₄×C₈	—	4	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	C₂×D₄	1	1	yes	characteristic
769	#95	C₂×D₄	1	1	yes	characteristic
770	#95	C₂×D₄	1	1	yes	characteristic
771	#95	C₂×D₄	1	1	yes	characteristic
772	#95	C₂×D₄	1	1	yes	characteristic
773	#95	C₂×D₄	1	1	yes	characteristic
774	#95	C₂×D₄	1	1	yes	characteristic
775	#95	C₂×D₄	1	1	yes	characteristic
776	C₂⁴	—	2	1	no	—
777	C₂⁴	—	2	1	no	—
778	C₂⁴	C₂²×D₄	1	1	yes	characteristic
779	C₂×Q₈	—	2	1	no	—
780	C₂×Q₈	—	2	1	no	—
781	C₂×Q₈	—	2	1	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	4	2	no	—
791	C₂×Q₈	—	4	2	no	—
792	C₂×Q₈	—	8	1	no	—
793	C₂×Q₈	C₂×#41	1	2	yes	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	—	4	2	no	—
807	C₂×D₄	—	4	2	no	—
808	C₂×D₄	—	4	2	no	—
809	C₂×D₄	—	8	1	no	—
810	C₂×D₄	—	8	1	no	—
811	C₂×D₄	C₂×#41	1	2	yes	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	—	4	1	no	—
837	C₂²×C₄	—	4	1	no	—
838	C₂²×C₄	—	4	2	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	—	4	2	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	8	1	no	—
849	C₂²×C₄	—	8	1	no	—
850	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
851	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
854	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
855	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
857	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
858	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
859	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
860	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
861	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
862	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
863	C₂²×C₄	C₂⁵	1	1	yes	characteristic
864	Q₁₆	—	4	4	no	—
865	SD₁₆	—	2	8	no	—
866	SD₁₆	—	4	4	no	—
867	D₈	—	4	4	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	—	2	1	no	—
870	C₂×C₈	—	2	1	no	—
871	C₂×C₈	—	2	1	no	—
872	C₂×C₈	—	2	1	no	—
873	C₂×C₈	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	no	—
879	C₂×C₈	—	2	1	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	—	4	4	no	—
887	C₂×C₈	—	4	4	no	—
888	C₂×C₈	C₂×#41	1	2	yes	—
889	C₂×C₈	C₂×#41	1	2	yes	—
890	C₂×C₈	C₂×#41	1	2	yes	—
891	C₂×C₈	C₂×#41	1	2	yes	—
892	C₂×C₈	C₂×#41	1	2	yes	—
893	C₂×C₈	C₂×#41	1	2	yes	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	4	1	no	—
918	C₄⋊C₄	—	4	1	no	—
919	C₄⋊C₄	—	4	1	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	2	no	—
922	C₄⋊C₄	—	4	2	no	—
923	C₄⋊C₄	—	4	2	no	—
924	C₄⋊C₄	—	4	2	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	—	4	2	no	—
928	C₄⋊C₄	—	4	2	no	—
929	C₄⋊C₄	—	4	2	no	—
930	C₄⋊C₄	—	4	2	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₄⋊C₄	—	4	2	no	—
933	C₄⋊C₄	—	4	2	no	—
934	C₄⋊C₄	—	4	2	no	—
935	C₄⋊C₄	—	4	2	no	—
936	C₄⋊C₄	—	8	1	no	—
937	C₄⋊C₄	—	8	1	no	—
938	C₄⋊C₄	—	8	1	no	—
939	C₄⋊C₄	—	8	1	no	—
940	C₄⋊C₄	—	8	1	no	—
941	C₄⋊C₄	—	8	1	no	—
942	C₄⋊C₄	—	8	1	no	—
943	C₄⋊C₄	C₂×#41	1	2	yes	—
944	C₄⋊C₄	C₂×#41	1	2	yes	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	4	1	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	—	4	2	no	—
952	C₂²⋊C₄	—	4	2	no	—
953	C₂²⋊C₄	—	4	2	no	—
954	C₂²⋊C₄	—	4	2	no	—
955	C₂²⋊C₄	—	4	2	no	—
956	C₂²⋊C₄	—	4	2	no	—
957	C₂²⋊C₄	—	4	2	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₂²⋊C₄	—	4	2	no	—
966	C₂²⋊C₄	—	4	2	no	—
967	C₂²⋊C₄	—	4	2	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	8	1	no	—
970	C₂²⋊C₄	—	8	1	no	—
971	C₂²⋊C₄	—	8	1	no	—
972	C₂²⋊C₄	—	8	1	no	—
973	C₂²⋊C₄	—	8	1	no	—
974	C₂²⋊C₄	—	8	1	no	—
975	C₂²⋊C₄	—	8	1	no	—
976	C₂²⋊C₄	—	8	1	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	4	1	no	—
991	C₄²	—	4	1	no	—
992	C₄²	—	4	1	no	—
993	C₄²	—	4	1	no	—
994	C₄²	—	4	1	no	—
995	C₄²	—	4	1	no	—
996	C₄²	—	4	1	no	—
997	C₄²	—	4	2	no	—
998	C₄²	—	4	2	no	—
999	C₄²	—	4	2	no	—
1000	C₄²	—	4	2	no	—
1001	C₄²	—	4	2	no	—
1002	C₄²	—	4	2	no	—
1003	C₄²	—	4	2	no	—
1004	C₄²	—	4	2	no	—
1005	C₄²	—	8	1	no	—
1006	C₄²	—	8	1	no	—
1007	C₄²	—	8	1	no	—
1008	C₄²	—	8	1	no	—
1009	C₄²	C₂×#41	1	2	yes	—
1010	C₄²	C₂×#41	1	2	yes	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	4	1	no	—
1019	C₂³	—	4	1	no	—
1020	C₂³	—	4	1	no	—
1021	C₂³	—	4	1	no	—
1022	C₂³	—	4	1	no	—
1023	C₂³	—	4	1	no	—
1024	C₂³	—	4	1	no	—
1025	C₂³	—	4	1	no	—
1026	C₂³	—	4	1	no	—
1027	C₂³	—	4	1	no	—
1028	C₂³	—	4	1	no	—
1029	C₂³	—	4	1	no	—
1030	C₂³	—	4	1	no	—
1031	C₂³	#575	1	2	yes	—
1032	C₂³	C₂³×D₄	1	1	yes	characteristic
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	4	1	no	—
1036	Q₈	—	4	1	no	—
1037	Q₈	—	4	1	no	—
1038	Q₈	—	4	1	no	—
1039	Q₈	—	4	1	no	—
1040	Q₈	—	4	1	no	—
1041	Q₈	—	8	4	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	4	1	no	—
1045	D₄	—	4	1	no	—
1046	D₄	—	4	1	no	—
1047	D₄	—	4	1	no	—
1048	D₄	—	4	1	no	—
1049	D₄	—	4	1	no	—
1050	D₄	—	8	4	no	—
1051	D₄	—	8	4	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	4	4	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	1	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	8	2	no	—
1136	C₂×C₄	—	8	4	no	—
1137	C₂×C₄	—	8	4	no	—
1138	C₂×C₄	—	8	4	no	—
1139	C₂×C₄	—	8	4	no	—
1140	C₂×C₄	#532	1	2	yes	—
1141	C₂×C₄	#532	1	2	yes	—
1142	C₂×C₄	#575	1	2	yes	—
1143	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1144	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1145	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1146	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1147	C₂×C₄	#585	1	1	yes	characteristic
1148	C₂×C₄	#585	1	1	yes	characteristic
1149	C₈	—	2	2	no	—
1150	C₈	—	2	2	no	—
1151	C₈	—	2	2	no	—
1152	C₈	—	4	1	no	—
1153	C₈	—	4	1	no	—
1154	C₈	—	4	1	no	—
1155	C₈	—	4	1	no	—
1156	C₈	#529	1	4	yes	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	8	1	no	—
1168	C₂²	—	8	1	no	—
1169	C₂²	—	8	1	no	—
1170	C₂²	—	8	1	no	—
1171	C₂²	—	8	1	no	—
1172	C₂²	—	8	1	no	—
1173	C₂²	—	8	1	no	—
1174	C₂²	—	8	1	no	—
1175	C₂²	—	8	1	no	—
1176	C₂²	—	8	1	no	—
1177	C₂²	—	8	1	no	—
1178	C₂²	C₂×#532	1	1	yes	characteristic
1179	C₂²	D₄×#41	1	1	yes	characteristic
1180	C₂²	D₄×#41	1	1	yes	characteristic
1181	C₂²	C₂×#575	1	1	yes	characteristic
1182	C₂²	C₂×#575	1	1	yes	characteristic
1183	C₂²	#3585	1	1	yes	characteristic
1184	C₂²	#3586	1	1	yes	characteristic
1185	C₄	—	2	2	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	2	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	2	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	2	no	—
1201	C₄	—	8	1	no	—
1202	C₄	—	8	1	no	—
1203	C₄	—	8	1	no	—
1204	C₄	—	8	1	no	—
1205	C₄	—	8	1	no	—
1206	C₄	—	8	1	no	—
1207	C₄	—	8	1	no	—
1208	C₄	—	8	1	no	—
1209	C₄	—	8	1	no	—
1210	C₄	—	8	1	no	—
1211	C₄	—	8	1	no	—
1212	C₄	C₂×#529	1	1	yes	characteristic
1213	C₄	#3455	1	1	yes	characteristic
1214	C₄	#3475	1	1	yes	characteristic
1215	C₄	#3480	1	1	yes	characteristic
1216	C₂	—	4	2	no	—
1217	C₂	—	8	2	no	—
1218	C₂	—	16	1	no	—
1219	C₂	#34914	1	1	yes	characteristic
1220	C₂	#60702	1	1	yes	characteristic
1221	C₂	#60703	1	1	yes	characteristic
1222	C₂	#61455	1	1	yes	characteristic
1223	C₂	#61456	1	1	yes	characteristic
1224	C₂	#61456	1	1	yes	characteristic
1225	C₂	#61460	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#1999	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×#117 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #34969	C₂	semidirect
2. #34915	C₂	semidirect
3. #29090	C₂	semidirect
4. #29087	C₂	semidirect
5. #29046	C₂	semidirect
6. #29040	C₂	semidirect
7. #29035	C₂	semidirect
8. #29033	C₂	semidirect
9. #28986	C₂	semidirect
11. #28018	C₂	semidirect
12. #28002	C₂	semidirect
13. #27837	C₂	semidirect
14. #27800	C₂	semidirect
15. #26486	C₂	semidirect
16. #26261	C₂	semidirect
18. #25041	C₂	semidirect
19. #23826	C₂	semidirect
20. #23821	C₂	semidirect
21. #23709	C₂	semidirect
23. #21731	C₂	semidirect
24. #21693	C₂	semidirect
25. #21528	C₂	semidirect
26. #21528	C₂	semidirect
27. #21288	C₂	semidirect
28. #21123	C₂	semidirect
29. #21122	C₂	semidirect
30. C₄×#440	C₂	semidirect
31. #20479	C₂	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#34969	2
#34915	2
#29090	2
#29087	2
#29046	2
#29040	2
#29035	2
#29033	2
#28986	2
#28983	2
#28018	2
#28002	2
#27837	2
#27800	2
#26486	2
#26261	2
#25411	2
#25041	2
#23826	2
#23821	2
#23709	2
#23708	2
#21731	2
#21693	2
#21528	2
#21288	2
#21123	2
#21122	2
C₄×#440	2
#20479	2